The desire to increase the amount of information that can be encoded onto a single photon has driven research in many areas of optics. One such area is the study of the orbital angular momentum (OAM) carried by a light beam. These beams have helical phase-fronts and carry an orbital angular momentum of l_hbar per photon, where the integer l is unbounded, giving a large state space in which to encode information. In the work that follows I discuss the development of new methods to measure the OAM carried by a light beam. An adaptation of a previously outlined interferometric technique is presented, resulting in a compact, robust measurement tool while dramatically reducing the number of degrees of freedom required for alignment. A new approach to sorting OAM is discussed, inspired by the simple example of the discrimination of plane waves focussed by a lens within direction space. This new approach is a telescopic system comprising two bespoke optical elements that transform OAM states into transverse momentum states; the various stages of development are outlined. Further to the development of this technique, investigations into the effects of misalignment and atmospheric turbulence on a communication link are presented. Outwith the area of optical communications, it is shown that by analysing the orbital angular momentum of light scattered from a spinning object we can observe a frequency shift many times greater than the rotation rate.